We also consider the problem of Bayesian A-optimal design, which has been previously studied via weak submodularity [1]}, [2]}, [3]}. In Appendix REF , we show that our parameter \(\beta \)  can be bounded by \(\gamma ^{-1}\)  for this problem, as well.
Given the relationship between \(\gamma \)  and \(\beta \)  for the problems we consider, it is natural to conjecture that \(\beta \)  may be bounded in some generic fashion for every weakly submodular function. In Appendix , we show that this is not the case by exhibiting a function on a ground set of size \(k\)  for which \(\beta \)  must be \(\Theta \!\left(k^{1-\gamma } \right)\) .
